1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Matrix help?

  1. Oct 13, 2008 #1
    Is is possible to represent a "square matrix" with the product of the constant and identity matrix of same order of given matrix


    EX:-A=[ ] 4x4 matrix

    can I make it something like this A=(K) I 4x4

    K= constant
    I=identity matrix
     
  2. jcsd
  3. Oct 13, 2008 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    It's not clear what you are asking. If I is the identity matrix, then (K)I= K. But what doe you mean by the "constant" matrix? A= (K) I= K only if A is already the "constant" matrix itself.
     
  4. Oct 13, 2008 #3
    No. There are tons of trivial counter examples. Any square matrix with components that are *not* along the diagonal.
     
  5. Oct 13, 2008 #4
    for example
    if the matrix A is some thing like this:-
    2 0 0
    0 2 0
    0 0 2 =====> A=(2)I
    where K=2
    I=identity matrix of order 3



    Now what I want to know is if matrix A is
    a b c
    d e f
    g h i =======>A=(k)I

    is it possible to shrink A in this form for a square matrix
    how can I find what exactly k is??
     
  6. Oct 13, 2008 #5

    statdad

    User Avatar
    Homework Helper

    You can't do what you want if the matrix [tex] A [/tex] does not have a form like these:

    [tex]
    \begin{bmatrix} 4 & 0\\0 & 4 \end{bmatrix}, \quad \begin{bmatrix} -3 & 0 & 0\\0 & -3 & 0\\0 & 0 & -3 \end{bmatrix}
    [/tex]

    So, even more directly, if you start with

    [tex]
    \begin{bmatrix} 4 & 2\\-8 & \pi \end{bmatrix}
    [/tex]

    you cannot write this as [tex] k I_2 [/tex] no matter how imaginative you are in selecting the number [tex] k [/tex].
     
  7. Oct 13, 2008 #6

    statdad

    User Avatar
    Homework Helper

    I must add - this is the point both HallsOfIvy and Tac-Tics were making.
     
  8. Oct 14, 2008 #7
    yeah I got the point
    @ all people thanks for your help
     
  9. Oct 19, 2008 #8
    so you saying that a nxn matrix can only be written as K * I where k is a constant is if it's diagonal elements are the same. (ie a diagonal matrix where the elements in the diagonal is equal)?
     
  10. Oct 20, 2008 #9

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Have you actually tried this multiplication? The number k times I is exactly a matrix with "k" along the diagaonal and zeros everywhere else. Why are you even asking such a question? It's a lot like asking repeatedly if 1+ 1= 3. DO it and see for yourself!
     
  11. Oct 20, 2008 #10

    statdad

    User Avatar
    Homework Helper

    This is an indubitable fact of mathematics.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Matrix help?
  1. Help with a matrix (Replies: 2)

Loading...